Solve a DE using power series (9) Find the recurrence relation (b) septie Solve the recurrence relation, that is, find an explicit formula for the wefficials (C) Define two independant solutions and write down the generel solution у"-гху'-гу=0 хто y" = 0
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- Find the power series solution for the equationy''-y=xProvide the recurrence relation for the coefficients and derive at least 3 non-zero terms of the solution. I just have no clue how to incorporate the =x as most power series I have worked with just =0A model for the number of lobsters caught per year is based on the assumption that the number of lobsters caught in a year is the average of the number caught in the two previous years. 1. Find a recurrence relation for {Ln}, where Ln is the number of lobsters caught in year n, under the assumption for this model. 2. Find Ln if 100,000 lobsters were caught in year 1 and 300,000 were caught in year 2.a.Seek power series solutions of the given differential equation about the given point x0; find the recurrence relation that the coefficients must satisfy. b.Find the first four nonzero terms in each of two solutions y1 and y2 (unless the series terminates sooner). c.By evaluating the Wronskian W[y1, y2](x0), show that y1 and y2 form a fundamental set of solutions. d.If possible, find the general term in each solution 9.(3 − x2)y″ − 3xy′ − y = 0, x0 = 0
- a.Seek power series solutions of the given differential equation about the given point x0; find the recurrence relation that the coefficients must satisfy. b.Find the first four nonzero terms in each of two solutions y1 and y2 (unless the series terminates sooner). c.By evaluating the Wronskian W[y1, y2](x0), show that y1 and y2 form a fundamental set of solutions. d.If possible, find the general term in each solution. 1.y″ − y = 0, x0 = 0by using the initial conditions given a. find the recurrence relation of the given ODE b. prove that the power series solution of y in powers of (x-1) for the given ODE is true. c. show that the given solution of y satisfies the original ODE and initial conditions [hint: you may want to use the method of substitution where t=x-1]a.Seek power series solutions of the given differential equation about the given point x0; find the recurrence relation that the coefficients must satisfy. b.Find the first four nonzero terms in each of two solutions y1 and y2 (unless the series terminates sooner). c.By evaluating the Wronskian W[y1, y2](x0), show that y1 and y2 form a fundamental set of solutions. d.If possible, find the general term in each solution 3.y″ − xy′ − y = 0, x0 = 0
- solve recurrence relation an = 5an-1 - 6an-2. Initial conditions a0 = 1 and a1 = 1 Help me fast......I will give Upvote....A . Suppose that there is a tree growing in a park. We observe that a bud of the tree will become a branch after one year. We also observe that each branch will produce a new bud on it after one year. Consider the tree in the park began as a single bud (the stump) and we let denote the number of branches and buds after years… Find a recurrence relation for the number of pairs of branches on the tree after Solve the recurrence relation found in part (a) using the characteristic equation.Solve the recurrence relation together with the initial conditions give an=an-2 for n≥2, a0=5, a1=-1
- Exapnd the function using Maclurin series expansion.Conjecture a general formula for Sn and based on the conjecture determine what the infinite series will result in.a) Determine if x0 = 0 is an ordinary or a singular point. If it is a singular point, determine if itis a regular or an irregular singular point. b) Based on your results in (a), use the appropriate method to determine two linearlyindependent series solutions about x0 = 0. Indicate, the indicial equation, the root(s) of theindicial equation, and the recurrence relation, where applicable.